Browsing by Subject "Difference equations."
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Item Boundary data smoothness for solutions of nonlocal boundary value problems.(Mathematical Sciences Publishers., 2011) Lyons, Jeffrey W.; Henderson, Johnny.; Mathematics.; Baylor University. Dept. of Mathematics.In this dissertation, we investigate boundary data smoothness for solutions of nonlocal boundary value problems over discrete and continuous domains. Essentially, we show that under certain conditions partial derivatives and differences exist, with respect to boundary conditions, for solutions of nonlocal boundary value problems and solve the variational equation in the derivative case and a specific linear difference equation in the difference case. Lastly, we provide a corollary and a few examples as well as some ideas for future work.Item Existence of positive solutions to singular right focal boundary value problems.(Orlando, FL : International Publications., 2005-05) Maroun, Mariette.; Henderson, Johnny.; Mathematics.; Baylor University. Dept. of Mathematics.In this dissetation, we seek positive solutions for the n^th order ordinary differential equation, y^(n)=f(x,y), satisfying the right focal boundary conditions, y^(i)(0)=y^(n-2)(p)=y^(n-1)(1)=0, i=0,...,n-3, where p is a fixed value between 1/2 and 1, and where f(x,y) has certain singulrities at x=0, at y=0, and possibly at y=infinity.Item Experimental investigation of a time scales linear feedback control theorem.(2008-03-03T17:25:15Z) Allen, Benjamin T.; Gravagne, Ian A.; Engineering.; Baylor University. Dept. of Electrical and Computer Engineering.Dynamic equations on time scales comprise an exciting new area of research in mathematics which promises applications in many areas, particularly control theory. This thesis describes the design and implementation of a simulator and real-time controller useful for experimentation with and demonstration of the applications of time scale control theory. Under the guidance of the Baylor time scales group, the system is used to test a time scales feedback control equation currently under research.